Mathematics
If x + 2y - 3 = 0, then find the value of x3 + 8y3 + 6x2y + 12xy2 - 125.
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Answer
Given,
x + 2y - 3 = 0
⇒ x + 2y = 3
Simplifying,
⇒ x3 + 8y3 + 6x2y + 12xy2 - 125
⇒ x3 + (2y)3 + 6xy(x + 2y) - 125
⇒ x3 + (2y)3 + 3.x.2y.(x + 2y) - 125
⇒ (x + 2y)3 - 125
⇒ 33 - 125
⇒ 27 - 125
⇒ -98.
Hence, the value of x3 + 8y3 + 6x2y + 12xy2 - 125 = -98.
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